Problem: If $m \angle AOC = 180^\circ$ and $m \angle AOB = 106^\circ$, what is $m \angle BOC$, in degrees? $106^\circ$ $O$ $A$ $C$ $B$
From the diagram, we see that $\angle AOB$ and $\angle BOC$ are supplementary angles. Therefore, $m \angle AOB + m \angle BOC = 180^\circ$ Thus, $m \angle BOC = 180^\circ - m \angle AOB = 180^\circ - 106^\circ = 74^\circ$.